English

On the higher derivatives of the inverse tangent function

Classical Analysis and ODEs 2017-12-12 v1

Abstract

In this paper, we find explicit formulas for higher order derivatives of the inverse tangent function. More precisely, we study polynomials which are induced from the higher-order derivatives of arctan(x). Successively, we give generating functions, recurrence relations and some particular properties for these polynomials. Connections to Chebyshev, Fibonacci, Lucas and Matching polynomials are established.

Keywords

Cite

@article{arxiv.1712.03521,
  title  = {On the higher derivatives of the inverse tangent function},
  author = {Mohamed Amine Boutiche and Mourad Rahmani},
  journal= {arXiv preprint arXiv:1712.03521},
  year   = {2017}
}